Finite Group Databasebeta

← #13078577

Subgroups — #13078577

Order 1408.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623056C211yesmaximal, characteristic
2#10623054C211yesmaximal, characteristic, complemented
3C11×#427C211yesmaximal, characteristic, complemented
4C2×#66885C211yesmaximal, characteristic, complemented
5#10622723C211yesmaximal, characteristic, complemented
6#10622614C211yesmaximal, characteristic, complemented
7#10622608C211yesmaximal, characteristic, complemented
8#10622498C212yesmaximal, complemented
9#10622495C212yesmaximal, complemented
10#10622479C212yesmaximal, complemented
11#10622476C212yesmaximal, complemented
12C2×#4339C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C22×C8×C11C2211yescharacteristic
15C11×#117C2211yescharacteristic
16C11×#117C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66948C2212yes—
20#66948C2212yes—
21#66945C2212yescomplemented
22C4⋊C4×D11C2212yescomplemented
23#66935—22no—
24(C22⋊D11)⋊C4—22no—
25#66928—21no—
26#66927—21no—
27C4×D44—21no—
28C4×Dic22—21no—
29C11×#107C2211yescharacteristic, complemented
30C11×#107C2211yescharacteristic, complemented
31C11×#106C2211yescharacteristic, complemented
32C11×#106C2211yescharacteristic, complemented
33#66885C2212yes—
34#66885C2212yes—
35(C2×D11)⋊C8C2212yescomplemented
36(C2×D11)⋊C8C2212yescomplemented
37#66873C2212yes—
38#66873C2212yes—
39#66872C2212yescomplemented
40#66871C2212yescomplemented
41C23×D11—21no—
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11D412yes—
44C22×Dic11—21no—
45#4339—22no—
46#4339—22no—
47C2×D44—22no—
48C2×D44—22no—
49C2×D44—21no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44D411yescharacteristic
53C2×D44C2312yes—
54C2×C4×D11—22no—
55C2×C4×D11C2312yes—
56C2×Dic22D411yescharacteristic
57C2×C8×C11—22no—
58C2×C8×C11C2311yescharacteristic
59C2×C8×C11C2311yescharacteristic
60C11×C4⋊C4C2311yescharacteristic
61C11×C4⋊C4C2311yescharacteristic
62C11×C4⋊C4C2311yescharacteristic
63C11×C4⋊C4C2311yescharacteristic
64C11×C22⋊C4—21no—
65C11×C22⋊C4—21no—
66C42×C11—21no—
67C42×C11—21no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4—22no—
70(C2×D11)⋊C4—22no—
71C4⋊Dic11—21no—
72C4⋊Dic11C2312yes—
73Dic11⋊C4—22no—
74C4×Dic11—22no—
75#4318—22no—
76C2×C11⋊C8C2312yes—
77#3096—111nomaximal, Sylow
78C23×C11C2×D411yescharacteristic
79C22×D11—22no—
80C22×D11—42no—
81C22×D11—81no—
82C22×D11—81no—
83C22×D11C2×D412yes—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11#4112yes—
90C2×C4×C11#4112yes—
91C2×C4×C11C2411yescharacteristic
92C22⋊D11—24no—
93C2×Dic11—22no—
94C2×Dic11—81no—
95C2×Dic11C2×D412yes—
96D44—22no—
97D44—22no—
98D44—22no—
99D44—42no—
100D44—82no—
101D44—82no—
102C4×D11—22no—
103C4×D11—22no—
104C4×D11—82no—
105Dic22—22no—
106C8×C11—21no—
107C8×C11—21no—
108C11⋊C8—22no—
109#535—111no—
110#520—111no—
111#482—112no—
112#482—112no—
113#481—112no—
114#480—112no—
115#428—111no—
116#427D1111yescharacteristic, complemented
117#418—111no—
118C2×#102—111no—
119#408—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11#12312yes—
123C22×C11C22×D411yescharacteristic
124C2×D11—22no—
125C2×D11—22no—
126C2×D11—22no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—84no—
131C4×C11—41no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11—41no—
135C4×C11#12312yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11C2×#4111yescharacteristic
138Dic11—22no—
139Dic11—42no—
140C2×#41—111no—
141C22×D4—111no—
142C2×M16—111no—
143C22×C8C2×D1111yescharacteristic
144#127—221no—
145#124—221no—
146#121—112no—
147#121—112no—
148#120—222no—
149C4×Q8—221no—
150C4×D4—221no—
151C4×D4—222no—
152#117—112no—
153#117C2×D1111yescharacteristic
154#117C2×D1111yescharacteristic
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
157#107—112no—
158#107C2×D1111yescharacteristic, complemented
159#107C2×D1111yescharacteristic, complemented
160#106—112no—
161#106C2×D1111yescharacteristic, complemented
162#106C2×D1111yescharacteristic, complemented
163#102—112no—
164#102—112no—
165#102—112no—
166#102—112no—
167C22⋊C8—112no—
168C22⋊C8—112no—
169C2×C11—22no—
170C2×C11C2×#12311yescharacteristic
171C2×C11#57611yescharacteristic
172C2×C11#57711yescharacteristic
173D11—42no—
174D11—82no—
175C24—221no—
176#41—222no—
177#41—222no—
178C2×Q8—111no—
179C2×D4—112no—
180C2×D4—111no—
181C2×D4—112no—
182C2×D4—222no—
183C2×D4—222no—
184C2×D4—222no—
185C2×D4—221no—
186C2×D4—222no—
187C22×C4—112no—
188C22×C4—222no—
189C22×C4—221no—
190C22×C4C22×D1111yescharacteristic
191M16—222no—
192C2×C8—22no—
193C2×C8—112no—
194C2×C8C22×D1111yescharacteristic
195C2×C8C22×D1111yescharacteristic
196C4⋊C4—112no—
197C4⋊C4—222no—
198C4⋊C4—221no—
199C4⋊C4C22×D1111yescharacteristic
200C4⋊C4C22×D1111yescharacteristic
201C4⋊C4C22×D1111yescharacteristic
202C4⋊C4C22×D1111yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—222no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C42—21no—
209C42—21no—
210C42—222no—
211C11#309611yescharacteristic, complemented, Sylow
212C23—112no—
213C23—222no—
214C23—442no—
215C23—881no—
216C23—881no—
217C23D4×D1111yescharacteristic
218Q8—222no—
219D4—224no—
220D4—222no—
221D4—222no—
222D4—222no—
223D4—442no—
224D4—882no—
225D4—882no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—112no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—882no—
235C2×C4—881no—
236C2×C4#433912yes—
237C2×C4D4×D1111yescharacteristic
238C2×C4#434312yes—
239C2×C4C23×D1111yescharacteristic
240C8—21no—
241C8—21no—
242C8—222no—
243C22—21no—
244C22—21no—
245C22—222no—
246C22—222no—
247C22—222no—
248C22—442no—
249C22—442no—
250C22—442no—
251C22—884no—
252C22#6694712yes—
253C22C2×D4×D1111yescharacteristic
254C4—41no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—222no—
259C4—442no—
260C4#6694712yes—
261C4C2×#433911yescharacteristic
262C4C2×#434311yescharacteristic
263C2—22no—
264C2—442no—
265C2—882no—
266C2C2×#6694711yescharacteristic
267C2#1062330011yescharacteristic
268C2#1062330111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#427C2
socleC22×C11C22×D4
prime radical#10623056C2
hypercenter#427D11
hypocenterC11#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10623054C2semidirect
3. C11×#427C2semidirect
4. C2×#66885C2semidirect
5. #10622723C2semidirect
6. #10622614C2semidirect
7. #10622608C2semidirect
8. #10622498C2semidirect
9. #10622495C2semidirect
10. #10622479C2semidirect
11. #10622476C2semidirect
21. #66945C22semidirect
22. C4⋊C4×D11C22semidirect
29. C11×#107C22semidirect
30. C11×#107C22semidirect
31. C11×#106C22semidirect
32. C11×#106C22semidirect
35. (C2×D11)⋊C8C22semidirect
36. (C2×D11)⋊C8C22semidirect
39. #66872C22semidirect
40. #66871C22semidirect
116. #427D11semidirect
158. #107C2×D11semidirect
159. #107C2×D11semidirect
161. #106C2×D11semidirect
162. #106C2×D11semidirect
211. C11#3096semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106230562
#106230542
C11×#4272
C2×#668852
#106227232
#106226142
#106226082
#106224982
#106224952
#106224792
#106224762
#309611